Answer:
The value of k = 20 for equation 2(4x+10)=8x+k to have infinitely many solutions.
Step-by-step explanation:
Given the expression
[tex]2(4x+10)=8x+k[/tex]
solving
[tex]2(4x+10)=8x+k[/tex]
[tex]8x+20 = 8x+k[/tex]
We know that the equations with infinitely many solutions have the same expressions on both sides
It means the value of k can be determined by further simplifying such as
[tex]8x+20 = 8x+k[/tex]
8x+20-8x = k
20 = k
Therefore, the value of k = 20 for equation 2(4x+10)=8x+k to have infinitely many solutions.
VERIFICATION:
Given
[tex]2(4x+10)=8x+k[/tex]
[tex]8x+20 = 8x+k[/tex]
Put k = 20 in the equation
[tex]8x+20 = 8x+20[/tex]
[tex]8x+20 - 8x+20 = 0[/tex]
[tex]0 = 0[/tex]
equations with infinitely many solutions have the same expressions on both sides.
This means the statement is always true.
